Transcript CAVITY QUANTUM ELECTRODYNAMICS

CAVITY QUANTUM
ELECTRODYNAMICS IN PHOTONIC
CRYSTAL STRUCTURES
Photonic Crystal Doctoral Course
PO-014
Summer Semester 2009
Konstantinos G. Lagoudakis
Outline
Light matter interaction
 Normal mode splitting
 Trapping light and matter in small volumes
 Experiments

How do we describe the interaction of
light and matter?


We have to get an expression of the total Hamiltonian
describing the system.
It will consist of three terms , one for the unperturbed
two level system, one for the free field, and one for
the interaction.
Hˆ total
o
†
†
†
ˆˆ

 ˆ z    ˆ ˆ  g ˆ ˆ  
2

γ
g
κ

We can calculate the eigenvalues of the
energy before and after the interaction



Excited atom with n photons present, or
atom in ground state with n+1 photons present.
Emission of photon is reversible: Exchange of energy
The states with which we describe the system are in the
general case:
 e, n 


g
,
n

1


Excited state with n photons
Ground state with n+1 photons
Energy level diagram
Coupled system
E1n
Ee,n
Eg,n+1
ħRn
ENERGY AXIS
Uncoupled system
E2n


Rn is the Quantum Rabi frequency
The effect is called Normal Mode Splitting
Energy level diagram
ħδ>0
Ee,n
Eg,n+1
ħδ≈0
Coupled system
E1n
ħ(Rn+δ)
ħδ<0
ENERGY AXIS
Uncoupled system
E2n


Rn is the Quantum Rabi frequency
The effect is called Normal Mode Splitting
Crossing and Anticrossing
Uncoupled system: tuning photon energy →
crossing with energy of 2level system
 Strongly coupled system: Anticrossing

Energy axis
E1n
Ee,n
ħRn
E2n
Eg,n+1
0
Detuning 
How would the spectrum look like?
We would see two delta-like function peaks
corresponding to the two new eigenenergies
Normalised Transmission

-3
-2
E-12n
0
E11n
2
3
In reality there are losses


There is a decay rate for the excited state of the atom (γ)
There is a decay rate for cavity photons (κ)
γ
κ
g





We define a quantity ξ as   4g 2  2   2
If ξ<1 weak coupling regime
If ξ≈1 intermediate coupling regime
For ξ>>1 Strong coupling regime

Realistic transmission spectrum
The peaks become broadened into Lorentzians
Normalised Transmission

E’1n
Lossless system
Realistic system
E’2n
Experimental observations of the
normal mode splitting
Source: H.J.Kimble “Observation of the normal-mode splitting for atoms in optical cavity” P.R.L. 68:8 1132, (1992)
TRANSMISSION
SPECTROMETER
SIDELIGHT
EMISSION
Source: M. S. Feld “Normal Mode Line Shapes for Atoms in Standing-Wave Optical Resonators ” P.R.L. 77:14 2901, (1996)
Source: M. S. Feld “Normal Mode Line Shapes for Atoms in Standing-Wave Optical Resonators ” P.R.L. 77:14 2901, (1996)
Up to now we investigated the effects
in atomic cavity QED
How can we manage this by means of
solid state photonic crystals??
 Replace atoms by QDs
 (atomic
 Replace
like spectra)
simple mirror cavities with PC
cavities

High Q factors and tiny mode volumes
Cavity QED in PC structures
 Cavity
construction
 placing QD
Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896 , (2007)
Tuning exciton resonance or cavity?
Two available options :
 Cavity tuning by condensation of innert
gases on surface of PC
 Exciton resonance tuning by varying a
gate voltage (when applicable)
Here the first method was applied
Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896 , (2007)
Tuning exciton resonance or cavity?
When tuning cavity resonant to QD exciton:


Anticrossing is
evidenced →
Signature of
strong coupling
Note the existence
of central peak
Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896 , (2007)
Cavity QED in PC structures


Complementary second order autocorrelation
measurements For the ‘trio’ of peaks
Antibunching of
emitted photons


(one photon at a
time)
Reduction of X
lifetime
Source: K. Hennesy “Quantum Nature of a strongly coupled single quantum dot-cavity system ” Nature 445 896 , (2007)
Alternate method :Tuning exciton
resonance
Changing Bias voltage
 Use of quantum confined stark effect
 Changes exciton resonance

A. Laucht "Electrical control of spontaneous emission and strong coupling for a single quantum dot" NJPh 11 023034, (2009)
Alternate method :Tuning exciton
resonance
Strong coupling
 No empty cavity peak?

A. Laucht "Electrical control of spontaneous emission and strong coupling for a single quantum dot" NJPh 11 023034, (2009)
Cavity QED in PC structures
 Advantages:
Monolithic structures
 Possibility of devices “photon on demand”
 Single photon gun
 Cavity QED on a chip
Summary
cavity QED suggests the appearance of effects
that cannot be described classically
 they are experimentally observable in two
fundamentally different communities
 these effects are of great interest because they
are direct evidence of the quantised nature of
field in cavities
